Why did David Cameron do it? It’s a question that still puzzles Lib Dems. I’m talking about The Day After The Election The Night Before, 7th May 2010, when the Conservative leader made his “big, open and comprehensive offer” to my party to join with his in forming a Coalition Government. Nick Clegg seized the opportunity with both hands and the rest is history.

What do we find so puzzling? Surely, Team Cameron would say, it’s all pretty obvious – the Conservatives had fallen just short of an overall majority. After 13 years of Labour mis-rule it was vital Gordon Brown & Co were ejected from government. The economy needed rescuing, our ‘broken society’ needed mending. This was no time for dallying: Britain needed a Conservative-led government and the Coalition was the means to this end.

All of which is reasonable enough. But it doesn’t answer the counter-factual: what would have happened if David Cameron hadn’t made his “big open and comprehensive offer”?

There were two other alternative histories waiting to be written. In one (the nightmare version with which Team Cameron scared Conservative backbenchers into submission in those five days in May) Labour and the Lib Dems cut a deal and thwarted the Conservatives’ quest for power. In the other (the nightmare version which still sends shivers down the spines of Lib Dems) the Conservatives struck out on their own and formed a minority government. What might have happened in either scenario?

Let’s imagine, then swiftly despatch, the notion Labour and the Lib Dems could have got it on together. Despite the attempted revisionism of Lord (Andrew) Adonis in his account, there was zero chance of this occurring. Between them, Labour and the Lib Dems could muster 315 seats, 11 short of a majority. Add to that the vocal opposition of Labour bigwigs like David Blunkett and John Reid and it’s a wonder the Lib Dems managed to maintain (for the sake of negotiating leverage) even a semblance of pretence a Lib/Lab pact was possible. Had by some miracle the deal been done, it would have unravelled as Alistair Darling’s prophesied “cuts worse than Thatcher’s” moved from tough-sounding rhetoric to rough reality. A coalition cobbled together on so flimsy a basis would quickly have collapsed.

A minority Conservative government, though: that would have been a different proposition.

Here’s how David Cameron could have played it. He would still have made what he would have termed a “big open and comprehensive offer” to the Lib Dems. But it would have been such a limited offer – two cabinet posts, including the poisoned chalice of Home Secretary for Nick Clegg, and no movement on electoral reform – he would have known neither Clegg nor his party could possibly accept it.

He would then have pinned the blame on the Lib Dems for the collapse of the talks: “The Lib Dems have, I’m sorry to say, shown they place party interest ahead of the national interest. We gave them a chance but it appears they are simply not ready to be a serious party of government. Their actions have confirmed what many of us have long suspected: a vote for the Lib Dems is a wasted vote. However, those voters who did place their trust in the Lib Dems can rest assured that I will lead a government of compassionate – and, yes, liberal – Conservatism.” His charge-sheet against Lib Dem triviality would have been cheerfully amplified by the media.

The Conservatives would have enjoyed a honeymoon, as most new governments do: the Coalition’s net approval rating stood at +13% when freshly minted (it’s currently -21%). The financial markets would have rallied behind Cameron and Osborne, offering a sheen of economic credibility. The Chancellor’s emergency budget would have laid responsibility for the “regrettable but necessary” austerity cuts squarely at the door of the previous Labour Government (notwithstanding the fact that Osborne had, just a couple of years earlier, pledged to follow its spending plans). Meanwhile, Labour – deprived of the unifying rallying-point of hating the Lib Dems – would have faced a much bloodier leadership election.

If Cameron were to be lucky in his enemies, the Lib Dems and Labour would have joined forces to vote down Osborne’s budget, thereby giving the Prime Minister exactly the pretext he needed to call a second election. “Only one party is prepared to face up to the task facing this nation,” Cameron would solemnly have intoned. “Labour and the Lib Dems believe they can wish away the economic crisis. A Conservative majority is now the only way we can provide the strong government so urgently needed.”

If, however, the Lib Dems had abstained on the budget then they would have proven Cameron’s charge they had nothing positive to offer. And if the Lib Dems had voted in favour of the Conservative budget they would have left the public scratching its head as to why the party had not joined the Conservatives in coalition and exerted far more influence on the government from within. A victory in the budget vote would, in any case, have deferred a second election only temporarily: Cameron would soon enough have found an alternative pretext (on welfare reform or immigration or Europe) for going to the polls in the autumn.

At that election I have little doubt the Conservatives would have increased their tally of MPs enough to win an overall majority: they would have needed to win only 10 more seats from the ranks of the cash-strapped and demoralised Labour and Lib Dems. Who would have bet against them doing so? In which case, the Conservatives would probably have now been gearing up for an autumn 2014 election on the back of a recovering economy, proudly – and solely – able to claim the credit for it. A second term of Conservative majority rule would beckon.

So why didn’t David Cameron do it? There are two explanations, I think. First, we shouldn’t under-estimate quite how much in May 2010 Cameron wanted to be Prime Minister – he saw his chance, and didn’t want to risk Labour and the Lib Dems ganging up to rob him of the job he wanted “because I think I’ll be good at it”.

And secondly, there was Cameron’s wish to avoid a repeat of John Major’s torrid time as a small-majority Prime Minister held to ransom by his truculent right-wing backbenchers. At least in the 1990s the John Redwoods, Bill Cashes and Teresa Gormans were a minority: these days the Philip Hollobones, Douglas Carswells and Peter Bones are well and truly in the ascendant, having captured the Conservative Party. How much more attractive to Cameron must have been the thought of the 80-plus majority the Coalition can muster? It also gave him the opportunity to ditch some of the more eccentric Conservative policies (inheritance tax cuts for millionaires are less popular now than they were in 2007) and blame the pesky Lib Dems for it all.

Here, then, is the irony for David Cameron as he approaches the May 2015 election. On even his most optimistic days, he can imagine only the Conservatives narrowly edging an overall majority next time. For sure, he wants an election victory to burnish his leadership CV. But his best hope now is what four-and-a-bit years ago was the nightmare he tried so desperately to dodge – a second term as Prime Minister pretending to lead a party which has long since set its own independent and ever more rightward direction.